The Digital Millennium Copyright Act is a US law passed in 1998 to combat internet piracy by criminalizing the unauthorized use of copyrighted material.
As an artist and content creator, you can therefore use it to take down unauthorized content of your work.
Although it is a US law, the DMCA actually applies to everyone - for example, YouTube's servers are in the US and content posted there must comply with US regulations. The majority of hosts, even in a country that does not directly apply the DMCA, are now used to remove content upon the receipt of a DMCA form, and the list of countries that do not apply it is getting smaller and smaller (fewer than a dozen countries worldwide by 2021).
These criticisms pale in comparison to a very simple fact: no one wants to see their work stolen - so that others can gain an audience and revenue from it. No one has the right to use your content without your permission - be it text, music, photos, video or software.
People who are explicitly in favor of freely sharing the content they have created can use many tools, such as open-source or Creative Commons copyleft licenses.
You decide whether you want to make your work available, not the "public."
Practices are changing, and streamers are now careful to use only royalty-free content, which also allows artists releasing royalty-free music to be showcased in ways they may never have imagined. Twitch has actually published a detailed FAQ on DMCA compliance on their platform, with a set of tools available to content creators.
By filling in a DMCA form
Your content does not need to be registered (but you may be asked for proof of ownership).
You must include a certain amount of information for the application to be considered:
You can also request the removal of the Google links pointing to your content.
The application itself is quite simple. However, you should be aware that you will be disclosing personal information (address, phone number) and that you will be legally bound - if you misrepresent yourself you may be prosecuted.
Furthermore, you can only file a DMCA claim if you have identified content that belongs to you online - so it requires a systematic search to check that your content is not somewhere online.
So if you want to make your life easier, don't hesitate to use a company that specializes in this area!